1. Initial speed of the satellite

For a circular orbit of radius $R$ around Earth,

$v_s = \sqrt{\frac{GM_E}{R}}$

where $G$ is the gravitational constant and $M_E$ is the mass of the Earth.

The problem states that the meteorite has the same speed just before collision:

$v_m = v_s = \sqrt{\frac{GM_E}{R}}$

2. Direction of velocities just before collision

• The satellite in circular orbit moves tangentially to the orbit.
• The meteorite is falling towards Earth, so its velocity is radially inward.

Thus, the two velocities are perpendicular.

3. Velocity after completely inelastic collision

Both bodies have mass $M$, and they stick together. By conservation of linear momentum:

$\vec V = \frac{M\vec v_s + M\vec v_m}{2M} = \frac{\vec v_s + \vec v_m}{2}$

Since $\vec v_s \perp \vec v_m$ and $|\vec v_s|=|\vec v_m|=v$,

$|\vec V| = \frac{1}{2}\sqrt{v^2+v^2} = \frac{v}{\sqrt{2}}$

So after collision, the combined body has speed

$V = \frac{1}{\sqrt{2}}\sqrt{\frac{GM_E}{R}} = \sqrt{\frac{GM_E}{2R}}$

4. Can the new orbit be circular?

For a circular orbit at radius $R$, the required speed is

$v_c = \sqrt{\frac{GM_E}{R}}$

But the new speed is

$V = \sqrt{\frac{GM_E}{2R}} < \sqrt{\frac{GM_E}{R}}$

So it cannot remain in the same circular orbit, nor can it move in another circular orbit at that instant because the velocity also has a radial component.

Hence, options A and C are ruled out.

5. Can it escape to infinity?

Escape speed at radius $R$ is

$v_{esc} = \sqrt{\frac{2GM_E}{R}}$

Clearly,

$V = \sqrt{\frac{GM_E}{2R}} < \sqrt{\frac{2GM_E}{R}} = v_{esc}$

So it cannot escape.

Thus, option B is ruled out.

6. Nature of the orbit from energy

Specific mechanical energy after collision is

$\epsilon = \frac{V^2}{2} - \frac{GM_E}{R}$

Using $V^2 = \frac{GM_E}{2R}$,

$\epsilon = \frac{1}{2}\cdot \frac{GM_E}{2R} - \frac{GM_E}{R} = \frac{GM_E}{4R} - \frac{GM_E}{R} = -\frac{3GM_E}{4R} < 0$

Negative total energy means the body remains in a bound orbit.

Since it is not circular and is bound, the orbit must be elliptical.

7. Checking options

• A: Same circular orbit of radius $R$ — False
• B: Escapes to infinity — False
• C: Circular orbit of different radius — False
• D: Elliptical orbit — True

Final Answer

$\boxed{\text{D: in an elliptical orbit}}$